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Occlusion criteria in tubes under transverse body forces

Published online by Cambridge University Press:  13 July 2011

ROBERT MANNING ,
STEVEN COLLICOTT  and
ROBERT FINN
ROBERT MANNING
Affiliation:
School of Aeronautics and Astronautics, Purdue University, W. Lafayette, IN 47907, USA
STEVEN COLLICOTT
Affiliation:
School of Aeronautics and Astronautics, Purdue University, W. Lafayette, IN 47907, USA
ROBERT FINN*
Affiliation:
Mathematics Department, Stanford University, Stanford, CA 94305-2125, USA
*
†Email address for correspondence: finn@math.stanford.edu
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Abstract

When a fluid in a tube is occluded, one finds a static configuration in which the occluding free surface of the fluid is an equilibrium capillary surface spanning the tube. We extend known criteria for existence and non-existence of such a surface, leading to an explicit mathematically rigorous occlusion criterion for cylindrical tubes in a transverse body force field, depending on the force magnitude and contact angle. For any contact angle γ ≠ π/2, we provide further an explicit design of a tube section, which will not occlude in a downward gravity field, regardless of the field strength. In addition, we derive a precise analytic occlusion criterion for liquid partially filling a circular vessel spinning about its axis.

JFM classification

Drops and Bubbles: Drops and Bubbles Multiphase and Particle-laden Flows: Gas/liquid flow Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 397 - 414
Copyright
Copyright © Cambridge University Press 2011

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